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## Main Question or Discussion Point

i seem to make these math threads alot ^.^. anyways, what math would you need to know to clearly understand basic QM? thanks.

- Thread starter Gecko
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- #1

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i seem to make these math threads alot ^.^. anyways, what math would you need to know to clearly understand basic QM? thanks.

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Tom Mattson

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That's for "basic" QM (which is what you asked for), so I am leaving out partial differential equations and group theory.

Why not PDEs? Well, while the Schrodinger equation is a PDE, you will be separating it into 4 ODEs (3 space+1 time), and all your ODE methods can be brought to bear.

Why not group theory? The only algebra you'll need for a first course in QM is on matrix manipulations, vector spaces, and linear transformations. You certainly will not have to know about SU(N), generators of groups, etc. The only thing from group theory that will come up is the idea of a nonabelian group, but this will all be self-contained in commutation relations.

For an advanced undergraduate course, you will need to supplement your mathematics with both PDEs and groups.

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Daniel.

PS.Integration of functions with maximum 3 variables and special functions (orthogonal polynomials,Bessel functions).

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http://superstringtheory.com/math/index.html

As a non-physicist myself, I'm unable to say how well the same courses would map onto what is needed for quantum mechanics. However, the section on mathematical background for graduate study in theoretical physics seems like it could be relevant.

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